In the title mol-ecule, C(17)H(12)N(6), the 2-pyridyl rings in the 3- and 4-positions and the 3-pyridyl ring in the 5-position make dihedral angles of 29.78 (16), 67.06 (16) and 32.97 (16)°, respectively, with the triazole group. The dihedral angle between the two 2-pyridyl rings is 65.72 (15)°. The dihedral angles between the 3-pyridyl ring and the two 2-pyridyl rings in the 3- and 4-positions...

In the title hydroxy-urea derivative, C(15)H(14)F(2)N(2)O(2), the dihedral angle between the two benzene rings is 48.64 (19)°. The urea group forms dihedral angles of 48.1 (2) and 79.2 (2)° with the two benzene rings. In the crystal, inversion dimers linked by pairs of N-H⋯O hydrogen bonds occur, and further N-H⋯O links lead to chains of molecules.

In the title mol-ecule, C(30)H(23)N(5)O(3)S, the 1,2,4-triazole ring is approximately planar (r.m.s. deviation = 0.006 Å), and forms dihedral angles of 66.0 (2), 65.1 (2), 30.1 (2) and 28.1 (2)° with the four phenyl rings. The phenyl ring of the benzyl group directly attached to the triazole ring is almost perpendicular to the nitro-phenyl ring, making a dihedral angle of 84.9 (2)°.

In the title compound, C14H14BrNO5, the ester group is disordered [occupancy ratio 0.52 (2):0.48 (2)]. The major component is nearly coplanar with the benzofuran plane, subtending a dihedral angle of 7.84 (2)°, while the amide group is twisted out of the benzofuran plane making a dihedral angle of 39.69 (2)°. An intra-molecular N-H⋯O hydrogen bond occurs. In the crystal, pairs of weak C-H⋯O hyd...

this article presents an analytic approach to study admissibility conditions related to classical full wavelet systems over finite fields using tools from computational harmonic analysis and theoretical linear algebra. it is shown that for a large class of non-zero window signals (wavelets), the generated classical full wavelet systems constitute a frame whose canonical dual are classical full ...

In this paper, we find a strong new restriction on the structure of CI-groups. We show that, if R is generalised dihedral group and CI-group, then for every odd prime p Sylow p-subgroup has order p, or 9. Consequently, any CI-group with quotient same restriction, that

In the title compound, C(17)H(14)ClF(2)NO(2), the amino-acrylo-yloxy group makes dihedral angles of 47.55 (11)° with the 4-chloro-phenyl group and 8.74 (12)° with the difluoro-phenyl group; the dihedral angle between the rings is 52.32 (11)°. The structure of the title compound reveals a Z configuration with respect to the C=C double bond in the amino-acrylate fragment. A bifurcated intramolecu...

In the title compound, C(18)H(15)N(3)O(2), the fused ring system is almost planar [the dihedral angle between the six-membered rings is 1.81 (6)°]. The 2-tolyl ring is approximately orthogonal to this plane [dihedral angle = 83.03 (7)°] as is the acetonitrile group [C-O-C-C torsion angle = 79.24 (14)°] which is also syn to the methyl substituent of the tolyl group. In the crystal, supra-molecul...

We study bipartite distance-regular Cayley graphs with diameter three or four. give sufficient conditions under which a graph can be constructed on the semidirect product of group — part this contains identity element and $\mathbb{Z}_{2}$. apply to case three, consider cases where are not satisfied for some specific groups such as dihedral group.We also extend result by Miklavič Potočnik that r...